LMFDB - Embedded newform 25.14.b.b.24.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [25,14,Mod(24,25)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("25.24"); S:= CuspForms(chi, 14); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 14, names="a")

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	25.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$26.8077322380$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 8933x^{4} + 19907716x^{2} + 350438400 $ x^6 + 8933x^4 + 19907716x^2 + 350438400
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{9}\cdot 5^{6} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.5
Root			$69.3208i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.14.b.b.24.2

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+90.6415i q^{2} -1125.79i q^{3} -23.8902 q^{4} +102044. q^{6} -324482. i q^{7} +740370. i q^{8} +326912. q^{9} -1.64726e6 q^{11} +26895.4i q^{12} +6.26700e6i q^{13} +2.94116e7 q^{14} -6.73040e7 q^{16} -1.66481e8i q^{17} +2.96318e7i q^{18} -3.12929e8 q^{19} -3.65300e8 q^{21} -1.49311e8i q^{22} -6.32351e8i q^{23} +8.33504e8 q^{24} -5.68051e8 q^{26} -2.16291e9i q^{27} +7.75194e6i q^{28} +2.82750e9 q^{29} +7.61629e9 q^{31} -3.54269e7i q^{32} +1.85448e9i q^{33} +1.50901e10 q^{34} -7.80998e6 q^{36} -1.99161e10i q^{37} -2.83644e10i q^{38} +7.05535e9 q^{39} -4.69877e10 q^{41} -3.31114e10i q^{42} -7.85897e9i q^{43} +3.93534e7 q^{44} +5.73173e10 q^{46} -8.31265e10i q^{47} +7.57704e10i q^{48} -8.39984e9 q^{49} -1.87423e11 q^{51} -1.49720e8i q^{52} -1.19285e11i q^{53} +1.96050e11 q^{54} +2.40237e11 q^{56} +3.52294e11i q^{57} +2.56289e11i q^{58} -4.20299e11 q^{59} +4.15504e11 q^{61} +6.90352e11i q^{62} -1.06077e11i q^{63} -5.48143e11 q^{64} -1.68093e11 q^{66} +1.02968e11i q^{67} +3.97727e9i q^{68} -7.11897e11 q^{69} -4.00383e11 q^{71} +2.42036e11i q^{72} +5.55011e11i q^{73} +1.80523e12 q^{74} +7.47593e9 q^{76} +5.34508e11i q^{77} +6.39508e11i q^{78} -1.60313e12 q^{79} -1.91379e12 q^{81} -4.25904e12i q^{82} -2.64201e11i q^{83} +8.72709e9 q^{84} +7.12349e11 q^{86} -3.18318e12i q^{87} -1.21958e12i q^{88} +3.69637e12 q^{89} +2.03353e12 q^{91} +1.51070e10i q^{92} -8.57437e12i q^{93} +7.53472e12 q^{94} -3.98834e10 q^{96} +1.00920e13i q^{97} -7.61375e11i q^{98} -5.38510e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 35752 q^{4} + 240752 q^{6} - 2572238 q^{9} - 13208008 q^{11} + 93125856 q^{14} + 399824416 q^{16} - 194982200 q^{19} + 876401472 q^{21} + 7780718400 q^{24} - 7493628088 q^{26} - 4472343700 q^{29}+ \cdots - 253574733016 q^{99}+O(q^{100}) $ 6 * q - 35752 * q^4 + 240752 * q^6 - 2572238 * q^9 - 13208008 * q^11 + 93125856 * q^14 + 399824416 * q^16 - 194982200 * q^19 + 876401472 * q^21 + 7780718400 * q^24 - 7493628088 * q^26 - 4472343700 * q^29 + 14965988752 * q^31 + 60472147976 * q^34 - 86723667704 * q^36 + 140377142144 * q^39 - 21505768868 * q^41 + 136791650336 * q^44 + 493656408672 * q^46 + 77913853258 * q^49 - 258739765888 * q^51 - 492243874400 * q^54 - 1045752902400 * q^56 + 110872847800 * q^59 + 992322785492 * q^61 - 6595130988672 * q^64 - 45767750336 * q^66 + 666758585664 * q^69 + 1043995756672 * q^71 + 4836647173016 * q^74 + 1243376100000 * q^76 - 5981273766400 * q^79 + 641098105526 * q^81 + 1628468261376 * q^84 + 4686627290192 * q^86 + 38846051916900 * q^89 - 13585044740368 * q^91 + 14007115751936 * q^94 - 4416662428928 * q^96 - 253574733016 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	90.6415i	1.00146i	0.865604	+	0.500729i	$0.166935\pi$
$2$	90.6415i	1.00146i	−0.865604	+	0.500729i	$0.833065\pi$
$3$	− 1125.79i	− 0.891601i	−0.895132	−	0.445801i	$-0.852919\pi$
$3$	− 1125.79i	− 0.891601i	0.895132	−	0.445801i	$-0.147081\pi$
$4$	−23.8902	−0.00291628
$5$	0	0
$5$	0	0
$6$	102044.	0.892900
$7$	− 324482.i	− 1.04245i	−0.853420	−	0.521223i	$-0.825476\pi$
$7$	− 324482.i	− 1.04245i	0.853420	−	0.521223i	$-0.174524\pi$
$8$	740370.i	0.998537i
$9$	326912.	0.205047
$10$	0	0
$11$	−1.64726e6	−0.280356	−0.140178	−	0.990126i	$-0.544768\pi$
$11$	−1.64726e6	−0.280356	−0.140178	+	0.990126i	$0.544768\pi$
$12$	26895.4i	0.00260016i
$13$	6.26700e6i	0.360104i	0.983657	+	0.180052i	$0.0576266\pi$
$13$	6.26700e6i	0.360104i	−0.983657	+	0.180052i	$0.942373\pi$
$14$	2.94116e7	1.04397
$15$	0	0
$16$	−6.73040e7	−1.00291
$17$	− 1.66481e8i	− 1.67281i	−0.548110	−	0.836406i	$-0.684653\pi$
$17$	− 1.66481e8i	− 1.67281i	0.548110	−	0.836406i	$-0.315347\pi$
$18$	2.96318e7i	0.205346i
$19$	−3.12929e8	−1.52598	−0.762988	−	0.646413i	$-0.776268\pi$
$19$	−3.12929e8	−1.52598	−0.762988	+	0.646413i	$0.776268\pi$
$20$	0	0
$21$	−3.65300e8	−0.929447
$22$	− 1.49311e8i	− 0.280765i
$23$	− 6.32351e8i	− 0.890692i	−0.895359	−	0.445346i	$-0.853081\pi$
$23$	− 6.32351e8i	− 0.890692i	0.895359	−	0.445346i	$-0.146919\pi$
$24$	8.33504e8	0.890296
$25$	0	0
$26$	−5.68051e8	−0.360629
$27$	− 2.16291e9i	− 1.07442i
$28$	7.75194e6i	0.00304007i
$29$	2.82750e9	0.882704	0.441352	−	0.897334i	$-0.354499\pi$
$29$	2.82750e9	0.882704	0.441352	+	0.897334i	$0.354499\pi$
$30$	0	0
$31$	7.61629e9	1.54132	0.770659	−	0.637247i	$-0.219927\pi$
$31$	7.61629e9	1.54132	0.770659	+	0.637247i	$0.219927\pi$
$32$	− 3.54269e7i	− 0.00583255i
$33$	1.85448e9i	0.249966i
$34$	1.50901e10	1.67525
$35$	0	0
$36$	−7.80998e6	−0.000597976 0
$37$	− 1.99161e10i	− 1.27613i	−0.769984	−	0.638063i	$-0.779736\pi$
$37$	− 1.99161e10i	− 1.27613i	0.769984	−	0.638063i	$-0.220264\pi$
$38$	− 2.83644e10i	− 1.52820i
$39$	7.05535e9	0.321069
$40$	0	0
$41$	−4.69877e10	−1.54486	−0.772430	−	0.635099i	$-0.780959\pi$
$41$	−4.69877e10	−1.54486	−0.772430	+	0.635099i	$0.780959\pi$
$42$	− 3.31114e10i	− 0.930801i
$43$	− 7.85897e9i	− 0.189592i	−0.995497	−	0.0947961i	$-0.969780\pi$
$43$	− 7.85897e9i	− 0.189592i	0.995497	−	0.0947961i	$-0.0302199\pi$
$44$	3.93534e7	0.000817599 0
$45$	0	0
$46$	5.73173e10	0.891990
$47$	− 8.31265e10i	− 1.12487i	−0.826840	−	0.562437i	$-0.809864\pi$
$47$	− 8.31265e10i	− 1.12487i	0.826840	−	0.562437i	$-0.190136\pi$
$48$	7.57704e10i	0.894194i
$49$	−8.39984e9	−0.0866955
$50$	0	0
$51$	−1.87423e11	−1.49148
$52$	− 1.49720e8i	− 0.00105017i
$53$	− 1.19285e11i	− 0.739255i	−0.929180	−	0.369628i	$-0.879485\pi$
$53$	− 1.19285e11i	− 0.739255i	0.929180	−	0.369628i	$-0.120515\pi$
$54$	1.96050e11	1.07599
$55$	0	0
$56$	2.40237e11	1.04092
$57$	3.52294e11i	1.36056i
$58$	2.56289e11i	0.883990i
$59$	−4.20299e11	−1.29724	−0.648620	−	0.761112i	$-0.724654\pi$
$59$	−4.20299e11	−1.29724	−0.648620	+	0.761112i	$0.724654\pi$
$60$	0	0
$61$	4.15504e11	1.03260	0.516299	−	0.856409i	$-0.327309\pi$
$61$	4.15504e11	1.03260	0.516299	+	0.856409i	$0.327309\pi$
$62$	6.90352e11i	1.54356i
$63$	− 1.06077e11i	− 0.213751i
$64$	−5.48143e11	−0.997067
$65$	0	0
$66$	−1.68093e11	−0.250330
$67$	1.02968e11i	0.139065i	0.997580	+	0.0695323i	$0.0221507\pi$
$67$	1.02968e11i	0.139065i	−0.997580	+	0.0695323i	$0.977849\pi$
$68$	3.97727e9i	0.00487839i
$69$	−7.11897e11	−0.794142
$70$	0	0
$71$	−4.00383e11	−0.370933	−0.185467	−	0.982651i	$-0.559380\pi$
$71$	−4.00383e11	−0.370933	−0.185467	+	0.982651i	$0.559380\pi$
$72$	2.42036e11i	0.204747i
$73$	5.55011e11i	0.429243i	0.976697	+	0.214621i	$0.0688517\pi$
$73$	5.55011e11i	0.429243i	−0.976697	+	0.214621i	$0.931148\pi$
$74$	1.80523e12	1.27798
$75$	0	0
$76$	7.47593e9	0.00445017
$77$	5.34508e11i	0.292257i
$78$	6.39508e11i	0.321537i
$79$	−1.60313e12	−0.741980	−0.370990	−	0.928637i	$-0.620982\pi$
$79$	−1.60313e12	−0.741980	−0.370990	+	0.928637i	$0.620982\pi$
$80$	0	0
$81$	−1.91379e12	−0.752908
$82$	− 4.25904e12i	− 1.54711i
$83$	− 2.64201e11i	− 0.0887005i	−0.999016	−	0.0443503i	$-0.985878\pi$
$83$	− 2.64201e11i	− 0.0887005i	0.999016	−	0.0443503i	$-0.0141218\pi$
$84$	8.72709e9	0.00271053
$85$	0	0
$86$	7.12349e11	0.189868
$87$	− 3.18318e12i	− 0.787020i
$88$	− 1.21958e12i	− 0.279946i
$89$	3.69637e12	0.788388	0.394194	−	0.919027i	$-0.371024\pi$
$89$	3.69637e12	0.788388	0.394194	+	0.919027i	$0.371024\pi$
$90$	0	0
$91$	2.03353e12	0.375390
$92$	1.51070e10i	0.00259751i
$93$	− 8.57437e12i	− 1.37424i
$94$	7.53472e12	1.12651
$95$	0	0
$96$	−3.98834e10	−0.00520030
$97$	1.00920e13i	1.23016i	0.788464	+	0.615081i	$0.210877\pi$
$97$	1.00920e13i	1.23016i	−0.788464	+	0.615081i	$0.789123\pi$
$98$	− 7.61375e11i	− 0.0868218i
$99$	−5.38510e11	−0.0574863
$100$	0	0
$101$	2.56737e12	0.240658	0.120329	−	0.992734i	$-0.461605\pi$
$101$	2.56737e12	0.240658	0.120329	+	0.992734i	$0.461605\pi$
$102$	− 1.69884e13i	− 1.49365i
$103$	1.21037e13i	0.998791i	0.866374	+	0.499395i	$0.166444\pi$
$103$	1.21037e13i	0.998791i	−0.866374	+	0.499395i	$0.833556\pi$
$104$	−4.63990e12	−0.359577
$105$	0	0
$106$	1.08122e13	0.740332
$107$	− 9.37488e12i	− 0.603909i	−0.953322	−	0.301954i	$-0.902361\pi$
$107$	− 9.37488e12i	− 0.603909i	0.953322	−	0.301954i	$-0.0976390\pi$
$108$	5.16724e10i	0.00313332i
$109$	2.49908e13	1.42727	0.713637	−	0.700516i	$-0.247047\pi$
$109$	2.49908e13	1.42727	0.713637	+	0.700516i	$0.247047\pi$
$110$	0	0
$111$	−2.24214e13	−1.13779
$112$	2.18390e13i	1.04548i
$113$	1.35600e13i	0.612703i	0.951918	+	0.306352i	$0.0991084\pi$
$113$	1.35600e13i	0.612703i	−0.951918	+	0.306352i	$0.900892\pi$
$114$	−3.19324e13	−1.36254
$115$	0	0
$116$	−6.75494e10	−0.00257421
$117$	2.04876e12i	0.0738384i
$118$	− 3.80966e13i	− 1.29913i
$119$	−5.40202e13	−1.74382
$120$	0	0
$121$	−3.18092e13	−0.921400
$122$	3.76619e13i	1.03410i
$123$	5.28985e13i	1.37740i
$124$	−1.81955e11	−0.00449492
$125$	0	0
$126$	9.61499e12	0.214062
$127$	1.16836e13i	0.247088i	0.992339	+	0.123544i	$0.0394261\pi$
$127$	1.16836e13i	0.247088i	−0.992339	+	0.123544i	$0.960574\pi$
$128$	− 4.99748e13i	− 1.00435i
$129$	−8.84758e12	−0.169041
$130$	0	0
$131$	5.12734e13	0.886398	0.443199	−	0.896423i	$-0.353843\pi$
$131$	5.12734e13	0.886398	0.443199	+	0.896423i	$0.353843\pi$
$132$	− 4.43038e10i	0 0.000728972i
$133$	1.01540e14i	1.59075i
$134$	−9.33319e12	−0.139267
$135$	0	0
$136$	1.23258e14	1.67036
$137$	7.15579e13i	0.924642i	0.886713	+	0.462321i	$0.152983\pi$
$137$	7.15579e13i	0.924642i	−0.886713	+	0.462321i	$0.847017\pi$
$138$	− 6.45275e13i	− 0.795299i
$139$	1.16286e14	1.36751	0.683754	−	0.729712i	$-0.260346\pi$
$139$	1.16286e14	1.36751	0.683754	+	0.729712i	$0.260346\pi$
$140$	0	0
$141$	−9.35833e13	−1.00294
$142$	− 3.62913e13i	− 0.371474i
$143$	− 1.03234e13i	− 0.100958i
$144$	−2.20025e13	−0.205644
$145$	0	0
$146$	−5.03070e13	−0.429868
$147$	9.45649e12i	0.0772978i
$148$	4.75800e11i	0.00372154i
$149$	1.43657e14	1.07552	0.537758	−	0.843099i	$-0.319271\pi$
$149$	1.43657e14	1.07552	0.537758	+	0.843099i	$0.319271\pi$
$150$	0	0
$151$	−1.99719e13	−0.137110	−0.0685551	−	0.997647i	$-0.521839\pi$
$151$	−1.99719e13	−0.137110	−0.0685551	+	0.997647i	$0.521839\pi$
$152$	− 2.31683e14i	− 1.52374i
$153$	− 5.44246e13i	− 0.343006i
$154$	−4.84486e13	−0.292683
$155$	0	0
$156$	−1.68554e11	−0.000936329 0
$157$	− 2.46452e14i	− 1.31336i	−0.754168	−	0.656682i	$-0.771959\pi$
$157$	− 2.46452e14i	− 1.31336i	0.754168	−	0.656682i	$-0.228041\pi$
$158$	− 1.45310e14i	− 0.743061i
$159$	−1.34291e14	−0.659121
$160$	0	0
$161$	−2.05187e14	−0.928499
$162$	− 1.73469e14i	− 0.754005i
$163$	1.33661e14i	0.558194i	0.960263	+	0.279097i	$0.0900352\pi$
$163$	1.33661e14i	0.558194i	−0.960263	+	0.279097i	$0.909965\pi$
$164$	1.12255e12	0.00450525
$165$	0	0
$166$	2.39476e13	0.0888298
$167$	1.57170e14i	0.560676i	0.959901	+	0.280338i	$0.0904465\pi$
$167$	1.57170e14i	0.560676i	−0.959901	+	0.280338i	$0.909553\pi$
$168$	− 2.70457e14i	− 0.928087i
$169$	2.63600e14	0.870325
$170$	0	0
$171$	−1.02300e14	−0.312897
$172$	1.87752e11i	0 0.000552904i
$173$	3.32272e14i	0.942309i	0.882051	+	0.471155i	$0.156163\pi$
$173$	3.32272e14i	0.942309i	−0.882051	+	0.471155i	$0.843837\pi$
$174$	2.88528e14	0.788167
$175$	0	0
$176$	1.10867e14	0.281172
$177$	4.73170e14i	1.15662i
$178$	3.35044e14i	0.789537i
$179$	−4.96701e14	−1.12863	−0.564313	−	0.825561i	$-0.690859\pi$
$179$	−4.96701e14	−1.12863	−0.564313	+	0.825561i	$0.690859\pi$
$180$	0	0
$181$	5.73895e14	1.21317	0.606585	−	0.795019i	$-0.292539\pi$
$181$	5.73895e14	1.21317	0.606585	+	0.795019i	$0.292539\pi$
$182$	1.84323e14i	0.375937i
$183$	− 4.67771e14i	− 0.920665i
$184$	4.68174e14	0.889388
$185$	0	0
$186$	7.77194e14	1.37624
$187$	2.74238e14i	0.468984i
$188$	1.98591e12i	0.00328045i
$189$	−7.01828e14	−1.12003
$190$	0	0
$191$	−9.21109e14	−1.37276	−0.686379	−	0.727244i	$-0.740801\pi$
$191$	−9.21109e14	−1.37276	−0.686379	+	0.727244i	$0.740801\pi$
$192$	6.17096e14i	0.888986i
$193$	8.88779e14i	1.23786i	0.785447	+	0.618929i	$0.212433\pi$
$193$	8.88779e14i	1.23786i	−0.785447	+	0.618929i	$0.787567\pi$
$194$	−9.14757e14	−1.23195
$195$	0	0
$196$	2.00674e11	0.000252829 0
$197$	4.70943e13i	0.0574035i	0.999588	+	0.0287017i	$0.00913730\pi$
$197$	4.70943e13i	0.0574035i	−0.999588	+	0.0287017i	$0.990863\pi$
$198$	− 4.88113e13i	− 0.0575701i
$199$	−4.94174e14	−0.564072	−0.282036	−	0.959404i	$-0.591010\pi$
$199$	−4.94174e14	−0.564072	−0.282036	+	0.959404i	$0.591010\pi$
$200$	0	0
$201$	1.15921e14	0.123990
$202$	2.32710e14i	0.241008i
$203$	− 9.17473e14i	− 0.920172i
$204$	4.47758e12	0.00434958
$205$	0	0
$206$	−1.09709e15	−1.00025
$207$	− 2.06723e14i	− 0.182634i
$208$	− 4.21795e14i	− 0.361151i
$209$	5.15477e14	0.427817
$210$	0	0
$211$	−1.22476e15	−0.955466	−0.477733	−	0.878505i	$-0.658541\pi$
$211$	−1.22476e15	−0.955466	−0.477733	+	0.878505i	$0.658541\pi$
$212$	2.84975e12i	0.00215588i
$213$	4.50748e14i	0.330725i
$214$	8.49754e14	0.604789
$215$	0	0
$216$	1.60136e15	1.07285
$217$	− 2.47135e15i	− 1.60674i
$218$	2.26520e15i	1.42935i
$219$	6.24828e14	0.382713
$220$	0	0
$221$	1.04334e15	0.602387
$222$	− 2.03231e15i	− 1.13945i
$223$	− 1.23977e15i	− 0.675087i	−0.941310	−	0.337544i	$-0.890404\pi$
$223$	− 1.23977e15i	− 0.675087i	0.941310	−	0.337544i	$-0.109596\pi$
$224$	−1.14954e13	−0.00608012
$225$	0	0
$226$	−1.22910e15	−0.613596
$227$	3.31953e14i	0.161031i	0.996753	+	0.0805154i	$0.0256566\pi$
$227$	3.31953e14i	0.161031i	−0.996753	+	0.0805154i	$0.974343\pi$
$228$	− 8.41636e12i	− 0.00396778i
$229$	1.92799e15	0.883433	0.441717	−	0.897155i	$-0.354370\pi$
$229$	1.92799e15	0.883433	0.441717	+	0.897155i	$0.354370\pi$
$230$	0	0
$231$	6.01746e14	0.260576
$232$	2.09339e15i	0.881412i
$233$	− 1.12721e15i	− 0.461522i	−0.973010	−	0.230761i	$-0.925878\pi$
$233$	− 1.12721e15i	− 0.461522i	0.973010	−	0.230761i	$-0.0741216\pi$
$234$	−1.85703e14	−0.0739460
$235$	0	0
$236$	1.00410e13	0.00378312
$237$	1.80479e15i	0.661550i
$238$	− 4.89648e15i	− 1.74636i
$239$	2.13044e15	0.739405	0.369703	−	0.929150i	$-0.379460\pi$
$239$	2.13044e15	0.739405	0.369703	+	0.929150i	$0.379460\pi$
$240$	0	0
$241$	3.70709e15	1.21877	0.609386	−	0.792874i	$-0.291416\pi$
$241$	3.70709e15	1.21877	0.609386	+	0.792874i	$0.291416\pi$
$242$	− 2.88324e15i	− 0.922743i
$243$	− 1.29385e15i	− 0.403128i
$244$	−9.92646e12	−0.00301134
$245$	0	0
$246$	−4.79480e15	−1.37941
$247$	− 1.96113e15i	− 0.549510i
$248$	5.63887e15i	1.53906i
$249$	−2.97435e14	−0.0790855
$250$	0	0
$251$	1.69706e15	0.428368	0.214184	−	0.976793i	$-0.431291\pi$
$251$	1.69706e15	0.428368	0.214184	+	0.976793i	$0.431291\pi$
$252$	2.53420e12i	0 0.000623358i
$253$	1.04165e15i	0.249711i
$254$	−1.05902e15	−0.247448
$255$	0	0
$256$	3.94010e13	0.00874877
$257$	3.42768e14i	0.0742053i	0.999311	+	0.0371027i	$0.0118129\pi$
$257$	3.42768e14i	0.0742053i	−0.999311	+	0.0371027i	$0.988187\pi$
$258$	− 8.01958e14i	− 0.169287i
$259$	−6.46243e15	−1.33029
$260$	0	0
$261$	9.24342e14	0.180996
$262$	4.64750e15i	0.887690i
$263$	4.63399e15i	0.863460i	0.902003	+	0.431730i	$0.142097\pi$
$263$	4.63399e15i	0.863460i	−0.902003	+	0.431730i	$0.857903\pi$
$264$	−1.37300e15	−0.249600
$265$	0	0
$266$	−9.20374e15	−1.59307
$267$	− 4.16134e15i	− 0.702927i
$268$	− 2.45993e12i	0 0.000405552i
$269$	5.38103e15	0.865915	0.432957	−	0.901414i	$-0.357470\pi$
$269$	5.38103e15	0.865915	0.432957	+	0.901414i	$0.357470\pi$
$270$	0	0
$271$	8.17255e15	1.25331	0.626653	−	0.779298i	$-0.284424\pi$
$271$	8.17255e15	1.25331	0.626653	+	0.779298i	$0.284424\pi$
$272$	1.12049e16i	1.67768i
$273$	− 2.28934e15i	− 0.334698i
$274$	−6.48612e15	−0.925990
$275$	0	0
$276$	1.70074e13	0.00231594
$277$	7.61841e14i	0.101332i	0.998716	+	0.0506659i	$0.0161344\pi$
$277$	7.61841e14i	0.101332i	−0.998716	+	0.0506659i	$0.983866\pi$
$278$	1.05403e16i	1.36950i
$279$	2.48985e15	0.316043
$280$	0	0
$281$	−9.73851e15	−1.18005	−0.590027	−	0.807384i	$-0.700883\pi$
$281$	−9.73851e15	−1.18005	−0.590027	+	0.807384i	$0.700883\pi$
$282$	− 8.48254e15i	− 1.00440i
$283$	− 1.30296e16i	− 1.50771i	−0.657038	−	0.753857i	$-0.728191\pi$
$283$	− 1.30296e16i	− 1.50771i	0.657038	−	0.753857i	$-0.271809\pi$
$284$	9.56522e12	0.00108175
$285$	0	0
$286$	9.35730e14	0.101105
$287$	1.52467e16i	1.61044i
$288$	− 1.15815e13i	− 0.00119595i
$289$	−1.78114e16	−1.79830
$290$	0	0
$291$	1.13615e16	1.09681
$292$	− 1.32593e13i	− 0.00125179i
$293$	− 4.27472e15i	− 0.394701i	−0.980333	−	0.197351i	$-0.936766\pi$
$293$	− 4.27472e15i	− 0.394701i	0.980333	−	0.197351i	$-0.0632337\pi$
$294$	−8.57151e14	−0.0774104
$295$	0	0
$296$	1.47453e16	1.27426
$297$	3.56289e15i	0.301221i
$298$	1.30213e16i	1.07708i
$299$	3.96295e15	0.320742
$300$	0	0
$301$	−2.55010e15	−0.197640
$302$	− 1.81029e15i	− 0.137310i
$303$	− 2.89033e15i	− 0.214571i
$304$	2.10614e16	1.53041
$305$	0	0
$306$	4.93313e15	0.343505
$307$	− 1.84450e16i	− 1.25742i	−0.777640	−	0.628709i	$-0.783583\pi$
$307$	− 1.84450e16i	− 1.25742i	0.777640	−	0.628709i	$-0.216417\pi$
$308$	− 1.27695e13i	0 0.000852303i
$309$	1.36262e16	0.890523
$310$	0	0
$311$	−2.21772e16	−1.38984	−0.694918	−	0.719089i	$-0.744559\pi$
$311$	−2.21772e16	−1.38984	−0.694918	+	0.719089i	$0.744559\pi$
$312$	5.22357e15i	0.320600i
$313$	− 2.02883e16i	− 1.21957i	−0.792567	−	0.609785i	$-0.791256\pi$
$313$	− 2.02883e16i	− 1.21957i	0.792567	−	0.609785i	$-0.208744\pi$
$314$	2.23388e16	1.31528
$315$	0	0
$316$	3.82990e13	0.00216382
$317$	− 1.93347e16i	− 1.07017i	−0.844798	−	0.535085i	$-0.820280\pi$
$317$	− 1.93347e16i	− 1.07017i	0.844798	−	0.535085i	$-0.179720\pi$
$318$	− 1.21723e16i	− 0.660081i
$319$	−4.65763e15	−0.247472
$320$	0	0
$321$	−1.05542e16	−0.538446
$322$	− 1.85985e16i	− 0.929852i
$323$	5.20968e16i	2.55267i
$324$	4.57208e13	0.00219569
$325$	0	0
$326$	−1.21152e16	−0.559008
$327$	− 2.81344e16i	− 1.27256i
$328$	− 3.47883e16i	− 1.54260i
$329$	−2.69731e16	−1.17262
$330$	0	0
$331$	4.61159e15	0.192739	0.0963693	−	0.995346i	$-0.469277\pi$
$331$	4.61159e15	0.192739	0.0963693	+	0.995346i	$0.469277\pi$
$332$	6.31180e12i	0 0.000258676i
$333$	− 6.51081e15i	− 0.261666i
$334$	−1.42461e16	−0.561493
$335$	0	0
$336$	2.45862e16	0.932150
$337$	3.91103e16i	1.45444i	0.686402	+	0.727222i	$0.259189\pi$
$337$	3.91103e16i	1.45444i	−0.686402	+	0.727222i	$0.740811\pi$
$338$	2.38931e16i	0.871593i
$339$	1.52658e16	0.546287
$340$	0	0
$341$	−1.25460e16	−0.432119
$342$	− 9.27264e15i	− 0.313353i
$343$	− 2.87132e16i	− 0.952071i
$344$	5.81854e15	0.189315
$345$	0	0
$346$	−3.01176e16	−0.943682
$347$	− 5.96375e15i	− 0.183391i	−0.995787	−	0.0916955i	$-0.970771\pi$
$347$	− 5.96375e15i	− 0.183391i	0.995787	−	0.0916955i	$-0.0292286\pi$
$348$	7.60467e13i	0.00229517i
$349$	−2.76636e15	−0.0819490	−0.0409745	−	0.999160i	$-0.513046\pi$
$349$	−2.76636e15	−0.0819490	−0.0409745	+	0.999160i	$0.513046\pi$
$350$	0	0
$351$	1.35550e16	0.386904
$352$	5.83574e13i	0.00163519i
$353$	1.98418e16i	0.545816i	0.962040	+	0.272908i	$0.0879854\pi$
$353$	1.98418e16i	0.545816i	−0.962040	+	0.272908i	$0.912015\pi$
$354$	−4.28889e16	−1.15831
$355$	0	0
$356$	−8.83068e13	−0.00229916
$357$	6.08156e16i	1.55479i
$358$	− 4.50217e16i	− 1.13027i
$359$	3.22798e16	0.795824	0.397912	−	0.917424i	$-0.369735\pi$
$359$	3.22798e16	0.795824	0.397912	+	0.917424i	$0.369735\pi$
$360$	0	0
$361$	5.58716e16	1.32860
$362$	5.20187e16i	1.21494i
$363$	3.58106e16i	0.821522i
$364$	−4.85815e13	−0.00109474
$365$	0	0
$366$	4.23995e16	0.922006
$367$	4.42436e16i	0.945194i	0.881279	+	0.472597i	$0.156683\pi$
$367$	4.42436e16i	0.945194i	−0.881279	+	0.472597i	$0.843317\pi$
$368$	4.25598e16i	0.893282i
$369$	−1.53608e16	−0.316770
$370$	0	0
$371$	−3.87060e16	−0.770634
$372$	2.04843e14i	0.00400768i
$373$	9.26267e16i	1.78086i	0.455125	+	0.890428i	$0.349595\pi$
$373$	9.26267e16i	1.78086i	−0.455125	+	0.890428i	$0.650405\pi$
$374$	−2.48574e16	−0.469667
$375$	0	0
$376$	6.15444e16	1.12323
$377$	1.77199e16i	0.317865i
$378$	− 6.36147e16i	− 1.12166i
$379$	3.71415e16	0.643732	0.321866	−	0.946785i	$-0.395690\pi$
$379$	3.71415e16	0.643732	0.321866	+	0.946785i	$0.395690\pi$
$380$	0	0
$381$	1.31533e16	0.220304
$382$	− 8.34907e16i	− 1.37476i
$383$	− 1.22127e16i	− 0.197706i	−0.995102	−	0.0988532i	$-0.968483\pi$
$383$	− 1.22127e16i	− 0.197706i	0.995102	−	0.0988532i	$-0.0315174\pi$
$384$	−5.62613e16	−0.895482
$385$	0	0
$386$	−8.05603e16	−1.23966
$387$	− 2.56919e15i	− 0.0388754i
$388$	− 2.41100e14i	− 0.00358750i
$389$	−7.53716e16	−1.10290	−0.551449	−	0.834209i	$-0.685925\pi$
$389$	−7.53716e16	−1.10290	−0.551449	+	0.834209i	$0.685925\pi$
$390$	0	0
$391$	−1.05275e17	−1.48996
$392$	− 6.21899e15i	− 0.0865686i
$393$	− 5.77233e16i	− 0.790314i
$394$	−4.26870e15	−0.0574871
$395$	0	0
$396$	1.28651e13	0.000167646 0
$397$	− 8.59809e16i	− 1.10221i	−0.834437	−	0.551104i	$-0.814207\pi$
$397$	− 8.59809e16i	− 1.10221i	0.834437	−	0.551104i	$-0.185793\pi$
$398$	− 4.47927e16i	− 0.564894i
$399$	1.14313e17	1.41831
$400$	0	0
$401$	−1.13598e17	−1.36437	−0.682186	−	0.731178i	$-0.738971\pi$
$401$	−1.13598e17	−1.36437	−0.682186	+	0.731178i	$0.738971\pi$
$402$	1.05072e16i	0.124171i
$403$	4.77313e16i	0.555035i
$404$	−6.13349e13	−0.000701825 0
$405$	0	0
$406$	8.31612e16	0.921513
$407$	3.28071e16i	0.357770i
$408$	− 1.38763e17i	− 1.48930i
$409$	3.50572e16	0.370318	0.185159	−	0.982709i	$-0.440720\pi$
$409$	3.50572e16	0.370318	0.185159	+	0.982709i	$0.440720\pi$
$410$	0	0
$411$	8.05594e16	0.824412
$412$	− 2.89159e14i	− 0.00291276i
$413$	1.36380e17i	1.35230i
$414$	1.87377e16	0.182900
$415$	0	0
$416$	2.22020e14	0.00210032
$417$	− 1.30914e17i	− 1.21927i
$418$	4.67236e16i	0.428440i
$419$	2.82535e15	0.0255083	0.0127541	−	0.999919i	$-0.495940\pi$
$419$	2.82535e15	0.0255083	0.0127541	+	0.999919i	$0.495940\pi$
$420$	0	0
$421$	8.17054e16	0.715183	0.357591	−	0.933878i	$-0.383598\pi$
$421$	8.17054e16	0.715183	0.357591	+	0.933878i	$0.383598\pi$
$422$	− 1.11014e17i	− 0.956859i
$423$	− 2.71750e16i	− 0.230652i
$424$	8.83154e16	0.738173
$425$	0	0
$426$	−4.08565e16	−0.331207
$427$	− 1.34824e17i	− 1.07643i
$428$	2.23968e14i	0.00176117i
$429$	−1.16220e16	−0.0900139
$430$	0	0
$431$	4.31353e16	0.324139	0.162069	−	0.986779i	$-0.448183\pi$
$431$	4.31353e16	0.324139	0.162069	+	0.986779i	$0.448183\pi$
$432$	1.45573e17i	1.07755i
$433$	− 6.25222e16i	− 0.455893i	−0.973674	−	0.227947i	$-0.926799\pi$
$433$	− 6.25222e16i	− 0.455893i	0.973674	−	0.227947i	$-0.0732011\pi$
$434$	2.24007e17	1.60908
$435$	0	0
$436$	−5.97034e14	−0.00416233
$437$	1.97881e17i	1.35917i
$438$	5.66353e16i	0.383271i
$439$	7.25265e16	0.483590	0.241795	−	0.970327i	$-0.422264\pi$
$439$	7.25265e16	0.483590	0.241795	+	0.970327i	$0.422264\pi$
$440$	0	0
$441$	−2.74601e15	−0.0177767
$442$	9.45698e16i	0.603265i
$443$	− 2.76459e17i	− 1.73783i	−0.494962	−	0.868914i	$-0.664818\pi$
$443$	− 2.76459e17i	− 1.73783i	0.494962	−	0.868914i	$-0.335182\pi$
$444$	5.35652e14	0.00331813
$445$	0	0
$446$	1.12375e17	0.676071
$447$	− 1.61728e17i	− 0.958931i
$448$	1.77863e17i	1.03939i
$449$	−2.46120e17	−1.41757	−0.708786	−	0.705424i	$-0.750757\pi$
$449$	−2.46120e17	−1.41757	−0.708786	+	0.705424i	$0.750757\pi$
$450$	0	0
$451$	7.74012e16	0.433112
$452$	− 3.23951e14i	− 0.00178682i
$453$	2.24843e16i	0.122248i
$454$	−3.00888e16	−0.161265
$455$	0	0
$456$	−2.60828e17	−1.35857
$457$	3.45983e17i	1.77664i	0.459226	+	0.888319i	$0.348127\pi$
$457$	3.45983e17i	1.77664i	−0.459226	+	0.888319i	$0.651873\pi$
$458$	1.74756e17i	0.884721i
$459$	−3.60084e17	−1.79731
$460$	0	0
$461$	−1.04114e17	−0.505188	−0.252594	−	0.967572i	$-0.581284\pi$
$461$	−1.04114e17	−0.505188	−0.252594	+	0.967572i	$0.581284\pi$
$462$	5.45432e16i	0.260956i
$463$	− 1.70140e17i	− 0.802656i	−0.915934	−	0.401328i	$-0.868549\pi$
$463$	− 1.70140e17i	− 0.802656i	0.915934	−	0.401328i	$-0.131451\pi$
$464$	−1.90302e17	−0.885271
$465$	0	0
$466$	1.02172e17	0.462195
$467$	− 1.84060e17i	− 0.821106i	−0.911837	−	0.410553i	$-0.865336\pi$
$467$	− 1.84060e17i	− 0.821106i	0.911837	−	0.410553i	$-0.134664\pi$
$468$	− 4.89452e13i	0 0.000215334i
$469$	3.34114e16	0.144968
$470$	0	0
$471$	−2.77454e17	−1.17100
$472$	− 3.11177e17i	− 1.29534i
$473$	1.29458e16i	0.0531534i
$474$	−1.63589e17	−0.662514
$475$	0	0
$476$	1.29055e15	0.00508546
$477$	− 3.89958e16i	− 0.151582i
$478$	1.93106e17i	0.740482i
$479$	2.13215e17	0.806562	0.403281	−	0.915076i	$-0.367870\pi$
$479$	2.13215e17	0.806562	0.403281	+	0.915076i	$0.367870\pi$
$480$	0	0
$481$	1.24814e17	0.459538
$482$	3.36016e17i	1.22055i
$483$	2.30998e17i	0.827851i
$484$	7.59928e14	0.00268706
$485$	0	0
$486$	1.17276e17	0.403715
$487$	3.74978e17i	1.27370i	0.770987	+	0.636851i	$0.219763\pi$
$487$	3.74978e17i	1.27370i	−0.770987	+	0.636851i	$0.780237\pi$
$488$	3.07626e17i	1.03109i
$489$	1.50475e17	0.497687
$490$	0	0
$491$	4.11003e17	1.32378	0.661889	−	0.749602i	$-0.269755\pi$
$491$	4.11003e17	1.32378	0.661889	+	0.749602i	$0.269755\pi$
$492$	− 1.26375e15i	− 0.00401689i
$493$	− 4.70725e17i	− 1.47660i
$494$	1.77760e17	0.550311
$495$	0	0
$496$	−5.12607e17	−1.54580
$497$	1.29917e17i	0.386678i
$498$	− 2.69600e16i	− 0.0792007i
$499$	−1.73839e17	−0.504072	−0.252036	−	0.967718i	$-0.581100\pi$
$499$	−1.73839e17	−0.504072	−0.252036	+	0.967718i	$0.581100\pi$
$500$	0	0
$501$	1.76941e17	0.499899
$502$	1.53824e17i	0.428992i
$503$	− 3.28753e17i	− 0.905062i	−0.891749	−	0.452531i	$-0.850521\pi$
$503$	− 3.28753e17i	− 0.905062i	0.891749	−	0.452531i	$-0.149479\pi$
$504$	7.85363e16	0.213438
$505$	0	0
$506$	−9.44167e16	−0.250075
$507$	− 2.96759e17i	− 0.775983i
$508$	− 2.79123e14i	0 0.000720579i
$509$	−6.89978e16	−0.175861	−0.0879305	−	0.996127i	$-0.528025\pi$
$509$	−6.89978e16	−0.175861	−0.0879305	+	0.996127i	$0.528025\pi$
$510$	0	0
$511$	1.80091e17	0.447463
$512$	− 4.05822e17i	− 0.995591i
$513$	6.76839e17i	1.63954i
$514$	−3.10690e16	−0.0743135
$515$	0	0
$516$	2.11370e14	0.000492970 0
$517$	1.36931e17i	0.315365i
$518$	− 5.85765e17i	− 1.33223i
$519$	3.74069e17	0.840164
$520$	0	0
$521$	8.38335e17	1.83642	0.918211	−	0.396092i	$-0.129634\pi$
$521$	8.38335e17	1.83642	0.918211	+	0.396092i	$0.129634\pi$
$522$	8.37838e16i	0.181260i
$523$	− 1.91687e17i	− 0.409573i	−0.978807	−	0.204786i	$-0.934350\pi$
$523$	− 1.91687e17i	− 0.409573i	0.978807	−	0.204786i	$-0.0656499\pi$
$524$	−1.22493e15	−0.00258499
$525$	0	0
$526$	−4.20032e17	−0.864719
$527$	− 1.26797e18i	− 2.57834i
$528$	− 1.24814e17i	− 0.250693i
$529$	1.04168e17	0.206668
$530$	0	0
$531$	−1.37401e17	−0.265996
$532$	− 2.42581e15i	− 0.00463907i
$533$	− 2.94472e17i	− 0.556311i
$534$	3.77191e17	0.703952
$535$	0	0
$536$	−7.62345e16	−0.138861
$537$	5.59183e17i	1.00628i
$538$	4.87744e17i	0.867177i
$539$	1.38368e16	0.0243056
$540$	0	0
$541$	−8.65938e17	−1.48492	−0.742462	−	0.669888i	$-0.766342\pi$
$541$	−8.65938e17	−1.48492	−0.742462	+	0.669888i	$0.766342\pi$
$542$	7.40773e17i	1.25513i
$543$	− 6.46087e17i	− 1.08166i
$544$	−5.89791e15	−0.00975675
$545$	0	0
$546$	2.07509e17	0.335185
$547$	− 1.16237e18i	− 1.85536i	−0.373382	−	0.927678i	$-0.621802\pi$
$547$	− 1.16237e18i	− 1.85536i	0.373382	−	0.927678i	$-0.378198\pi$
$548$	− 1.70953e15i	− 0.00269652i
$549$	1.35833e17	0.211731
$550$	0	0
$551$	−8.84806e17	−1.34698
$552$	− 5.27067e17i	− 0.792980i
$553$	5.20187e17i	0.773475i
$554$	−6.90545e16	−0.101479
$555$	0	0
$556$	−2.77809e15	−0.00398804
$557$	1.02746e17i	0.145783i	0.997340	+	0.0728917i	$0.0232227\pi$
$557$	1.02746e17i	0.145783i	−0.997340	+	0.0728917i	$0.976777\pi$
$558$	2.25684e17i	0.316504i
$559$	4.92522e16	0.0682730
$560$	0	0
$561$	3.08736e17	0.418146
$562$	− 8.82714e17i	− 1.18177i
$563$	7.17343e17i	0.949341i	0.880164	+	0.474671i	$0.157433\pi$
$563$	7.17343e17i	0.949341i	−0.880164	+	0.474671i	$0.842567\pi$
$564$	2.23572e15	0.00292485
$565$	0	0
$566$	1.18102e18	1.50991
$567$	6.20992e17i	0.784867i
$568$	− 2.96431e17i	− 0.370391i
$569$	1.25353e17	0.154848	0.0774238	−	0.996998i	$-0.475331\pi$
$569$	1.25353e17	0.154848	0.0774238	+	0.996998i	$0.475331\pi$
$570$	0	0
$571$	−1.00269e17	−0.121069	−0.0605344	−	0.998166i	$-0.519280\pi$
$571$	−1.00269e17	−0.121069	−0.0605344	+	0.998166i	$0.519280\pi$
$572$	2.46628e14i	0 0.000294421i
$573$	1.03698e18i	1.22395i
$574$	−1.38198e18	−1.61278
$575$	0	0
$576$	−1.79194e17	−0.204446
$577$	1.36098e18i	1.53535i	0.640839	+	0.767675i	$0.278587\pi$
$577$	1.36098e18i	1.53535i	−0.640839	+	0.767675i	$0.721413\pi$
$578$	− 1.61445e18i	− 1.80092i
$579$	1.00058e18	1.10368
$580$	0	0
$581$	−8.57285e16	−0.0924656
$582$	1.02983e18i	1.09841i
$583$	1.96495e17i	0.207255i
$584$	−4.10913e17	−0.428614
$585$	0	0
$586$	3.87468e17	0.395276
$587$	6.87785e16i	0.0693913i	0.999398	+	0.0346956i	$0.0110462\pi$
$587$	6.87785e16i	0.0693913i	−0.999398	+	0.0346956i	$0.988954\pi$
$588$	− 2.25917e14i	0 0.000225422i
$589$	−2.38336e18	−2.35201
$590$	0	0
$591$	5.30185e16	0.0511810
$592$	1.34043e18i	1.27984i
$593$	− 3.46338e17i	− 0.327073i	−0.986537	−	0.163536i	$-0.947710\pi$
$593$	− 3.46338e17i	− 0.327073i	0.986537	−	0.163536i	$-0.0522901\pi$
$594$	−3.22946e17	−0.301660
$595$	0	0
$596$	−3.43200e15	−0.00313651
$597$	5.56338e17i	0.502928i
$598$	3.59208e17i	0.321209i
$599$	1.08982e18	0.964004	0.482002	−	0.876170i	$-0.339910\pi$
$599$	1.08982e18	0.964004	0.482002	+	0.876170i	$0.339910\pi$
$600$	0	0
$601$	2.73058e17	0.236358	0.118179	−	0.992992i	$-0.462294\pi$
$601$	2.73058e17	0.236358	0.118179	+	0.992992i	$0.462294\pi$
$602$	− 2.31145e17i	− 0.197928i
$603$	3.36615e16i	0.0285148i
$604$	4.77133e14	0.000399852 0
$605$	0	0
$606$	2.61984e17	0.214883
$607$	1.19160e18i	0.966951i	0.875358	+	0.483476i	$0.160626\pi$
$607$	1.19160e18i	0.966951i	−0.875358	+	0.483476i	$0.839374\pi$
$608$	1.10861e16i	0.00890032i
$609$	−1.03289e18	−0.820426
$610$	0	0
$611$	5.20954e17	0.405072
$612$	1.30021e15i	0.00100030i
$613$	3.63023e17i	0.276338i	0.990409	+	0.138169i	$0.0441217\pi$
$613$	3.63023e17i	0.276338i	−0.990409	+	0.138169i	$0.955878\pi$
$614$	1.67189e18	1.25925
$615$	0	0
$616$	−3.95734e17	−0.291829
$617$	− 6.06720e17i	− 0.442726i	−0.975192	−	0.221363i	$-0.928949\pi$
$617$	− 6.06720e17i	− 0.442726i	0.975192	−	0.221363i	$-0.0710505\pi$
$618$	1.23510e18i	0.891821i
$619$	2.29300e18	1.63838	0.819190	−	0.573523i	$-0.194424\pi$
$619$	2.29300e18	1.63838	0.819190	+	0.573523i	$0.194424\pi$
$620$	0	0
$621$	−1.36772e18	−0.956979
$622$	− 2.01017e18i	− 1.39186i
$623$	− 1.19941e18i	− 0.821852i
$624$	−4.74854e17	−0.322003
$625$	0	0
$626$	1.83896e18	1.22135
$627$	− 5.80320e17i	− 0.381442i
$628$	5.88779e15i	0.00383014i
$629$	−3.31566e18	−2.13472
$630$	0	0
$631$	3.33398e17	0.210268	0.105134	−	0.994458i	$-0.466473\pi$
$631$	3.33398e17	0.210268	0.105134	+	0.994458i	$0.466473\pi$
$632$	− 1.18691e18i	− 0.740894i
$633$	1.37883e18i	0.851895i
$634$	1.75253e18	1.07173
$635$	0	0
$636$	3.20823e15	0.00192218
$637$	− 5.26418e16i	− 0.0312194i
$638$	− 4.22175e17i	− 0.247832i
$639$	−1.30890e17	−0.0760589
$640$	0	0
$641$	−8.91188e17	−0.507449	−0.253724	−	0.967277i	$-0.581656\pi$
$641$	−8.91188e17	−0.507449	−0.253724	+	0.967277i	$0.581656\pi$
$642$	− 9.56648e17i	− 0.539230i
$643$	5.58943e17i	0.311886i	0.987766	+	0.155943i	$0.0498416\pi$
$643$	5.58943e17i	0.311886i	−0.987766	+	0.155943i	$0.950158\pi$
$644$	4.90195e15	0.00270776
$645$	0	0
$646$	−4.72213e18	−2.55639
$647$	− 1.62698e18i	− 0.871973i	−0.899953	−	0.435987i	$-0.856399\pi$
$647$	− 1.62698e18i	− 0.871973i	0.899953	−	0.435987i	$-0.143601\pi$
$648$	− 1.41691e18i	− 0.751806i
$649$	6.92344e17	0.363690
$650$	0	0
$651$	−2.78223e18	−1.43257
$652$	− 3.19319e15i	− 0.00162785i
$653$	− 6.71206e17i	− 0.338782i	−0.985549	−	0.169391i	$-0.945820\pi$
$653$	− 6.71206e17i	− 0.338782i	0.985549	−	0.169391i	$-0.0541800\pi$
$654$	2.55015e18	1.27441
$655$	0	0
$656$	3.16246e18	1.54935
$657$	1.81439e17i	0.0880150i
$658$	− 2.44488e18i	− 1.17433i
$659$	1.08505e18	0.516053	0.258027	−	0.966138i	$-0.416928\pi$
$659$	1.08505e18	0.516053	0.258027	+	0.966138i	$0.416928\pi$
$660$	0	0
$661$	2.34214e18	1.09220	0.546100	−	0.837720i	$-0.316112\pi$
$661$	2.34214e18	1.09220	0.546100	+	0.837720i	$0.316112\pi$
$662$	4.18002e17i	0.193019i
$663$	− 1.17458e18i	− 0.537089i
$664$	1.95606e17	0.0885707
$665$	0	0
$666$	5.90150e17	0.262047
$667$	− 1.78797e18i	− 0.786217i
$668$	− 3.75481e15i	− 0.00163509i
$669$	−1.39573e18	−0.601909
$670$	0	0
$671$	−6.84444e17	−0.289495
$672$	1.29415e16i	0.00542104i
$673$	7.92495e17i	0.328775i	0.986396	+	0.164387i	$0.0525647\pi$
$673$	7.92495e17i	0.328775i	−0.986396	+	0.164387i	$0.947435\pi$
$674$	−3.54502e18	−1.45656
$675$	0	0
$676$	−6.29745e15	−0.00253811
$677$	2.35105e18i	0.938503i	0.883065	+	0.469251i	$0.155476\pi$
$677$	2.35105e18i	0.938503i	−0.883065	+	0.469251i	$0.844524\pi$
$678$	1.38371e18i	0.547083i
$679$	3.27469e18	1.28238
$680$	0	0
$681$	3.73711e17	0.143575
$682$	− 1.13719e18i	− 0.432748i
$683$	− 3.22912e17i	− 0.121717i	−0.998146	−	0.0608583i	$-0.980616\pi$
$683$	− 3.22912e17i	− 0.121717i	0.998146	−	0.0608583i	$-0.0193838\pi$
$684$	2.44397e15	0.000912496 0
$685$	0	0
$686$	2.60261e18	0.953459
$687$	− 2.17052e18i	− 0.787670i
$688$	5.28940e17i	0.190144i
$689$	7.47563e17	0.266209
$690$	0	0
$691$	3.36976e18	1.17758	0.588792	−	0.808284i	$-0.299604\pi$
$691$	3.36976e18	1.17758	0.588792	+	0.808284i	$0.299604\pi$
$692$	− 7.93803e15i	− 0.00274804i
$693$	1.74737e17i	0.0599265i
$694$	5.40564e17	0.183658
$695$	0	0
$696$	2.35673e18	0.785868
$697$	7.82257e18i	2.58426i
$698$	− 2.50747e17i	− 0.0820684i
$699$	−1.26901e18	−0.411494
$700$	0	0
$701$	−5.38800e18	−1.71499	−0.857493	−	0.514495i	$-0.827979\pi$
$701$	−5.38800e18	−1.71499	−0.857493	+	0.514495i	$0.827979\pi$
$702$	1.22865e18i	0.387468i
$703$	6.23233e18i	1.94734i
$704$	9.02936e17	0.279534
$705$	0	0
$706$	−1.79849e18	−0.546611
$707$	− 8.33067e17i	− 0.250873i
$708$	− 1.13041e16i	− 0.00337303i
$709$	1.40376e18	0.415044	0.207522	−	0.978230i	$-0.433460\pi$
$709$	1.40376e18	0.415044	0.207522	+	0.978230i	$0.433460\pi$
$710$	0	0
$711$	−5.24082e17	−0.152141
$712$	2.73668e18i	0.787234i
$713$	− 4.81617e18i	− 1.37284i
$714$	−5.51242e18	−1.55706
$715$	0	0
$716$	1.18663e16	0.00329139
$717$	− 2.39843e18i	− 0.659254i
$718$	2.92589e18i	0.796984i
$719$	1.38614e18	0.374170	0.187085	−	0.982344i	$-0.440096\pi$
$719$	1.38614e18	0.374170	0.187085	+	0.982344i	$0.440096\pi$
$720$	0	0
$721$	3.92742e18	1.04119
$722$	5.06429e18i	1.33054i
$723$	− 4.17342e18i	− 1.08666i
$724$	−1.37104e16	−0.00353794
$725$	0	0
$726$	−3.24593e18	−0.822719
$727$	− 4.20824e18i	− 1.05712i	−0.848894	−	0.528562i	$-0.822731\pi$
$727$	− 4.20824e18i	− 1.05712i	0.848894	−	0.528562i	$-0.177269\pi$
$728$	1.50557e18i	0.374840i
$729$	−4.50781e18	−1.11234
$730$	0	0
$731$	−1.30837e18	−0.317152
$732$	1.11751e16i	0.00268492i
$733$	7.61043e17i	0.181231i	0.995886	+	0.0906156i	$0.0288835\pi$
$733$	7.61043e17i	0.181231i	−0.995886	+	0.0906156i	$0.971117\pi$
$734$	−4.01031e18	−0.946571
$735$	0	0
$736$	−2.24022e16	−0.00519500
$737$	− 1.69616e17i	− 0.0389877i
$738$	− 1.39233e18i	− 0.317231i
$739$	−6.25215e18	−1.41202	−0.706010	−	0.708202i	$-0.749507\pi$
$739$	−6.25215e18	−1.41202	−0.706010	+	0.708202i	$0.749507\pi$
$740$	0	0
$741$	−2.20783e18	−0.489944
$742$	− 3.50838e18i	− 0.771757i
$743$	5.60504e18i	1.22223i	0.791543	+	0.611113i	$0.209278\pi$
$743$	5.60504e18i	1.22223i	−0.791543	+	0.611113i	$0.790722\pi$
$744$	6.34821e18	1.37223
$745$	0	0
$746$	−8.39583e18	−1.78345
$747$	− 8.63703e16i	− 0.0181878i
$748$	− 6.55160e15i	− 0.00136769i
$749$	−3.04199e18	−0.629543
$750$	0	0
$751$	4.79388e18	0.975053	0.487526	−	0.873108i	$-0.337899\pi$
$751$	4.79388e18	0.975053	0.487526	+	0.873108i	$0.337899\pi$
$752$	5.59475e18i	1.12814i
$753$	− 1.91053e18i	− 0.381933i
$754$	−1.60616e18	−0.318329
$755$	0	0
$756$	1.67668e16	0.00326632
$757$	− 2.47656e18i	− 0.478328i	−0.970979	−	0.239164i	$-0.923127\pi$
$757$	− 2.47656e18i	− 0.478328i	0.970979	−	0.239164i	$-0.0768733\pi$
$758$	3.36656e18i	0.644669i
$759$	1.17268e18	0.222643
$760$	0	0
$761$	1.02209e19	1.90761	0.953804	−	0.300430i	$-0.0971301\pi$
$761$	1.02209e19	1.90761	0.953804	+	0.300430i	$0.0971301\pi$
$762$	1.19224e18i	0.220625i
$763$	− 8.10906e18i	− 1.48786i
$764$	2.20055e16	0.00400335
$765$	0	0
$766$	1.10698e18	0.197994
$767$	− 2.63402e18i	− 0.467142i
$768$	− 4.43574e16i	− 0.00780042i
$769$	9.71765e18	1.69449	0.847247	−	0.531199i	$-0.178258\pi$
$769$	9.71765e18	1.69449	0.847247	+	0.531199i	$0.178258\pi$
$770$	0	0
$771$	3.85886e17	0.0661616
$772$	− 2.12331e16i	− 0.00360995i
$773$	6.33996e18i	1.06886i	0.845213	+	0.534429i	$0.179473\pi$
$773$	6.33996e18i	1.06886i	−0.845213	+	0.534429i	$0.820527\pi$
$774$	2.32875e17	0.0389320
$775$	0	0
$776$	−7.47184e18	−1.22836
$777$	7.27536e18i	1.18609i
$778$	− 6.83180e18i	− 1.10450i
$779$	1.47038e19	2.35742
$780$	0	0
$781$	6.59536e17	0.103994
$782$	− 9.54225e18i	− 1.49213i
$783$	− 6.11563e18i	− 0.948396i
$784$	5.65343e17	0.0869476
$785$	0	0
$786$	5.23213e18	0.791465
$787$	− 6.11756e17i	− 0.0917789i	−0.998947	−	0.0458894i	$-0.985388\pi$
$787$	− 6.11756e17i	− 0.0917789i	0.998947	−	0.0458894i	$-0.0146122\pi$
$788$	− 1.12509e15i	0 0.000167405i
$789$	5.21691e18	0.769862
$790$	0	0
$791$	4.39999e18	0.638711
$792$	− 3.98696e17i	− 0.0574022i
$793$	2.60396e18i	0.371843i
$794$	7.79344e18	1.10381
$795$	0	0
$796$	1.18059e16	0.00164499
$797$	− 1.19147e18i	− 0.164665i	−0.996605	−	0.0823327i	$-0.973763\pi$
$797$	− 1.19147e18i	− 0.164665i	0.996605	−	0.0823327i	$-0.0262370\pi$
$798$	1.03615e19i	1.42038i
$799$	−1.38390e19	−1.88170
$800$	0	0
$801$	1.20839e18	0.161657
$802$	− 1.02967e19i	− 1.36636i
$803$	− 9.14249e17i	− 0.120341i
$804$	−2.76937e15	−0.000361590 0
$805$	0	0
$806$	−4.32644e18	−0.555844
$807$	− 6.05792e18i	− 0.772051i
$808$	1.90080e18i	0.240305i
$809$	−7.74613e18	−0.971447	−0.485724	−	0.874112i	$-0.661444\pi$
$809$	−7.74613e18	−0.971447	−0.485724	+	0.874112i	$0.661444\pi$
$810$	0	0
$811$	−4.31453e18	−0.532474	−0.266237	−	0.963908i	$-0.585780\pi$
$811$	−4.31453e18	−0.532474	−0.266237	+	0.963908i	$0.585780\pi$
$812$	2.19186e16i	0.00268348i
$813$	− 9.20061e18i	− 1.11745i
$814$	−2.97368e18	−0.358291
$815$	0	0
$816$	1.26143e19	1.49582
$817$	2.45930e18i	0.289313i
$818$	3.17764e18i	0.370858i
$819$	6.64786e17	0.0769726
$820$	0	0
$821$	−1.32454e19	−1.50950	−0.754752	−	0.656011i	$-0.772243\pi$
$821$	−1.32454e19	−1.50950	−0.754752	+	0.656011i	$0.772243\pi$
$822$	7.30203e18i	0.825613i
$823$	− 1.59982e19i	− 1.79461i	−0.441407	−	0.897307i	$-0.645520\pi$
$823$	− 1.59982e19i	− 1.79461i	0.441407	−	0.897307i	$-0.354480\pi$
$824$	−8.96118e18	−0.997329
$825$	0	0
$826$	−1.23617e19	−1.35427
$827$	7.72194e18i	0.839345i	0.907676	+	0.419672i	$0.137855\pi$
$827$	7.72194e18i	0.839345i	−0.907676	+	0.419672i	$0.862145\pi$
$828$	4.93865e15i	0 0.000532612i
$829$	8.75341e18	0.936640	0.468320	−	0.883559i	$-0.344859\pi$
$829$	8.75341e18	0.936640	0.468320	+	0.883559i	$0.344859\pi$
$830$	0	0
$831$	8.57676e17	0.0903476
$832$	− 3.43522e18i	− 0.359048i
$833$	1.39842e18i	0.145025i
$834$	1.18662e19	1.22105
$835$	0	0
$836$	−1.23148e16	−0.00124764
$837$	− 1.64734e19i	− 1.65603i
$838$	2.56094e17i	0.0255454i
$839$	−1.14368e19	−1.13201	−0.566007	−	0.824400i	$-0.691513\pi$
$839$	−1.14368e19	−1.13201	−0.566007	+	0.824400i	$0.691513\pi$
$840$	0	0
$841$	−2.26589e18	−0.220834
$842$	7.40590e18i	0.716225i
$843$	1.09636e19i	1.05214i
$844$	2.92598e16	0.00278641
$845$	0	0
$846$	2.46319e18	0.230988
$847$	1.03215e19i	0.960511i
$848$	8.02839e18i	0.741405i
$849$	−1.46686e19	−1.34428
$850$	0	0
$851$	−1.25940e19	−1.13663
$852$	− 1.07685e16i	0 0.000964487i
$853$	− 9.31629e17i	− 0.0828084i	−0.999142	−	0.0414042i	$-0.986817\pi$
$853$	− 9.31629e17i	− 0.0828084i	0.999142	−	0.0414042i	$-0.0131831\pi$
$854$	1.22206e19	1.07800
$855$	0	0
$856$	6.94088e18	0.603025
$857$	− 9.56376e18i	− 0.824619i	−0.911044	−	0.412309i	$-0.864722\pi$
$857$	− 9.56376e18i	− 0.824619i	0.911044	−	0.412309i	$-0.135278\pi$
$858$	− 1.05344e18i	− 0.0901450i
$859$	−7.17114e18	−0.609022	−0.304511	−	0.952509i	$-0.598493\pi$
$859$	−7.17114e18	−0.609022	−0.304511	+	0.952509i	$0.598493\pi$
$860$	0	0
$861$	1.71646e19	1.43587
$862$	3.90985e18i	0.324611i
$863$	1.34010e19i	1.10425i	0.833761	+	0.552125i	$0.186183\pi$
$863$	1.34010e19i	1.10425i	−0.833761	+	0.552125i	$0.813817\pi$
$864$	−7.66253e16	−0.00626661
$865$	0	0
$866$	5.66711e18	0.456557
$867$	2.00520e19i	1.60337i
$868$	5.90411e16i	0.00468572i
$869$	2.64078e18	0.208019
$870$	0	0
$871$	−6.45302e17	−0.0500778
$872$	1.85024e19i	1.42518i
$873$	3.29920e18i	0.252241i
$874$	−1.79362e19	−1.36115
$875$	0	0
$876$	−1.49272e16	−0.00111610
$877$	8.23622e18i	0.611266i	0.952149	+	0.305633i	$0.0988681\pi$
$877$	8.23622e18i	0.611266i	−0.952149	+	0.305633i	$0.901132\pi$
$878$	6.57391e18i	0.484295i
$879$	−4.81246e18	−0.351916
$880$	0	0
$881$	7.58214e18	0.546322	0.273161	−	0.961968i	$-0.411931\pi$
$881$	7.58214e18	0.546322	0.273161	+	0.961968i	$0.411931\pi$
$882$	− 2.48902e17i	− 0.0178026i
$883$	− 1.22388e19i	− 0.868946i	−0.900685	−	0.434473i	$-0.856935\pi$
$883$	− 1.22388e19i	− 0.868946i	0.900685	−	0.434473i	$-0.143065\pi$
$884$	−2.49255e16	−0.00175673
$885$	0	0
$886$	2.50587e19	1.74036
$887$	− 2.48370e18i	− 0.171236i	−0.996328	−	0.0856182i	$-0.972713\pi$
$887$	− 2.48370e18i	− 0.171236i	0.996328	−	0.0856182i	$-0.0272865\pi$
$888$	− 1.66002e19i	− 1.13613i
$889$	3.79112e18	0.257576
$890$	0	0
$891$	3.15252e18	0.211083
$892$	2.96184e16i	0.00196875i
$893$	2.60127e19i	1.71653i
$894$	1.46593e19	0.960329
$895$	0	0
$896$	−1.62159e19	−1.04698
$897$	− 4.46146e18i	− 0.285974i
$898$	− 2.23087e19i	− 1.41964i
$899$	2.15350e19	1.36053
$900$	0	0
$901$	−1.98588e19	−1.23664
$902$	7.01576e18i	0.433743i
$903$	2.87088e18i	0.176216i
$904$	−1.00394e19	−0.611807
$905$	0	0
$906$	−2.03801e18	−0.122426
$907$	6.93837e18i	0.413819i	0.978360	+	0.206909i	$0.0663405\pi$
$907$	6.93837e18i	0.413819i	−0.978360	+	0.206909i	$0.933659\pi$
$908$	− 7.93042e15i	0 0.000469611i
$909$	8.39303e17	0.0493462
$910$	0	0
$911$	−4.63486e18	−0.268638	−0.134319	−	0.990938i	$-0.542885\pi$
$911$	−4.63486e18	−0.268638	−0.134319	+	0.990938i	$0.542885\pi$
$912$	− 2.37108e19i	− 1.36452i
$913$	4.35208e17i	0.0248678i
$914$	−3.13604e19	−1.77923
$915$	0	0
$916$	−4.60600e16	−0.00257634
$917$	− 1.66373e19i	− 0.924023i
$918$	− 3.26386e19i	− 1.79992i
$919$	4.92534e18	0.269703	0.134851	−	0.990866i	$-0.456944\pi$
$919$	4.92534e18	0.269703	0.134851	+	0.990866i	$0.456944\pi$
$920$	0	0
$921$	−2.07653e19	−1.12112
$922$	− 9.43705e18i	− 0.505924i
$923$	− 2.50920e18i	− 0.133575i
$924$	−1.43758e16	−0.000759914 0
$925$	0	0
$926$	1.54217e19	0.803826
$927$	3.95683e18i	0.204799i
$928$	− 1.00169e17i	− 0.00514841i
$929$	1.91203e19	0.975870	0.487935	−	0.872880i	$-0.337750\pi$
$929$	1.91203e19	0.975870	0.487935	+	0.872880i	$0.337750\pi$
$930$	0	0
$931$	2.62855e18	0.132295
$932$	2.69293e16i	0.00134593i
$933$	2.49669e19i	1.23918i
$934$	1.66835e19	0.822303
$935$	0	0
$936$	−1.51684e18	−0.0737304
$937$	− 4.30002e18i	− 0.207569i	−0.994600	−	0.103785i	$-0.966905\pi$
$937$	− 4.30002e18i	− 0.207569i	0.994600	−	0.103785i	$-0.0330953\pi$
$938$	3.02846e18i	0.145179i
$939$	−2.28404e19	−1.08737
$940$	0	0
$941$	5.18107e18	0.243269	0.121635	−	0.992575i	$-0.461186\pi$
$941$	5.18107e18	0.243269	0.121635	+	0.992575i	$0.461186\pi$
$942$	− 2.51489e19i	− 1.17270i
$943$	2.97128e19i	1.37600i
$944$	2.82878e19	1.30101
$945$	0	0
$946$	−1.17343e18	−0.0532309
$947$	− 1.94885e19i	− 0.878020i	−0.898482	−	0.439010i	$-0.855329\pi$
$947$	− 1.94885e19i	− 0.878020i	0.898482	−	0.439010i	$-0.144671\pi$
$948$	− 4.31168e16i	− 0.00192927i
$949$	−3.47825e18	−0.154572
$950$	0	0
$951$	−2.17669e19	−0.954165
$952$	− 3.99950e19i	− 1.74127i
$953$	− 2.96510e19i	− 1.28214i	−0.767483	−	0.641070i	$-0.778491\pi$
$953$	− 2.96510e19i	− 1.28214i	0.767483	−	0.641070i	$-0.221509\pi$
$954$	3.53464e18	0.151803
$955$	0	0
$956$	−5.08965e16	−0.00215631
$957$	5.24353e18i	0.220646i
$958$	1.93262e19i	0.807737i
$959$	2.32193e19	0.963890
$960$	0	0
$961$	3.35903e19	1.37566
$962$	1.13134e19i	0.460208i
$963$	− 3.06476e18i	− 0.123830i
$964$	−8.85631e16	−0.00355428
$965$	0	0
$966$	−2.09380e19	−0.829057
$967$	− 1.25349e18i	− 0.0493004i	−0.999696	−	0.0246502i	$-0.992153\pi$
$967$	− 1.25349e18i	− 0.0493004i	0.999696	−	0.0246502i	$-0.00784719\pi$
$968$	− 2.35506e19i	− 0.920052i
$969$	5.86502e19	2.27596
$970$	0	0
$971$	−2.17263e19	−0.831879	−0.415940	−	0.909392i	$-0.636547\pi$
$971$	−2.17263e19	−0.831879	−0.415940	+	0.909392i	$0.636547\pi$
$972$	3.09103e16i	0.00117563i
$973$	− 3.77327e19i	− 1.42555i
$974$	−3.39886e19	−1.27556
$975$	0	0
$976$	−2.79651e19	−1.03560
$977$	2.56555e19i	0.943768i	0.881661	+	0.471884i	$0.156426\pi$
$977$	2.56555e19i	0.943768i	−0.881661	+	0.471884i	$0.843574\pi$
$978$	1.36393e19i	0.498412i
$979$	−6.08889e18	−0.221030
$980$	0	0
$981$	8.16977e18	0.292659
$982$	3.72539e19i	1.32571i
$983$	1.02856e19i	0.363608i	0.983335	+	0.181804i	$0.0581936\pi$
$983$	1.02856e19i	0.363608i	−0.983335	+	0.181804i	$0.941806\pi$
$984$	−3.91645e19	−1.37538
$985$	0	0
$986$	4.26672e19	1.47875
$987$	3.03661e19i	1.04551i
$988$	4.68517e16i	0.00160253i
$989$	−4.96963e18	−0.168868
$990$	0	0
$991$	3.91892e19	1.31428	0.657140	−	0.753769i	$-0.271766\pi$
$991$	3.91892e19	1.31428	0.657140	+	0.753769i	$0.271766\pi$
$992$	− 2.69821e17i	− 0.00898981i
$993$	− 5.19170e18i	− 0.171846i
$994$	−1.17759e19	−0.387242
$995$	0	0
$996$	7.10578e15	0.000230636 0
$997$	− 1.60895e19i	− 0.518829i	−0.965766	−	0.259414i	$-0.916470\pi$
$997$	− 1.60895e19i	− 0.518829i	0.965766	−	0.259414i	$-0.0835296\pi$
$998$	− 1.57570e19i	− 0.504807i
$999$	−4.30768e19	−1.37110

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.14.b.b.24.5		6
5.2	odd	4		5.14.a.b.1.1	✓	3
5.3	odd	4		25.14.a.b.1.3		3
5.4	even	2	inner	25.14.b.b.24.2		6
15.2	even	4		45.14.a.e.1.3		3
20.7	even	4		80.14.a.g.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.14.a.b.1.1	✓	3	5.2	odd	4
25.14.a.b.1.3		3	5.3	odd	4
25.14.b.b.24.2		6	5.4	even	2	inner
25.14.b.b.24.5		6	1.1	even	1	trivial
45.14.a.e.1.3		3	15.2	even	4
80.14.a.g.1.3		3	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+90.6415i q^{2} -1125.79i q^{3} -23.8902 q^{4} +102044. q^{6} -324482. i q^{7} +740370. i q^{8} +326912. q^{9} -1.64726e6 q^{11} +26895.4i q^{12} +6.26700e6i q^{13} +2.94116e7 q^{14} -6.73040e7 q^{16} -1.66481e8i q^{17} +2.96318e7i q^{18} -3.12929e8 q^{19} -3.65300e8 q^{21} -1.49311e8i q^{22} -6.32351e8i q^{23} +8.33504e8 q^{24} -5.68051e8 q^{26} -2.16291e9i q^{27} +7.75194e6i q^{28} +2.82750e9 q^{29} +7.61629e9 q^{31} -3.54269e7i q^{32} +1.85448e9i q^{33} +1.50901e10 q^{34} -7.80998e6 q^{36} -1.99161e10i q^{37} -2.83644e10i q^{38} +7.05535e9 q^{39} -4.69877e10 q^{41} -3.31114e10i q^{42} -7.85897e9i q^{43} +3.93534e7 q^{44} +5.73173e10 q^{46} -8.31265e10i q^{47} +7.57704e10i q^{48} -8.39984e9 q^{49} -1.87423e11 q^{51} -1.49720e8i q^{52} -1.19285e11i q^{53} +1.96050e11 q^{54} +2.40237e11 q^{56} +3.52294e11i q^{57} +2.56289e11i q^{58} -4.20299e11 q^{59} +4.15504e11 q^{61} +6.90352e11i q^{62} -1.06077e11i q^{63} -5.48143e11 q^{64} -1.68093e11 q^{66} +1.02968e11i q^{67} +3.97727e9i q^{68} -7.11897e11 q^{69} -4.00383e11 q^{71} +2.42036e11i q^{72} +5.55011e11i q^{73} +1.80523e12 q^{74} +7.47593e9 q^{76} +5.34508e11i q^{77} +6.39508e11i q^{78} -1.60313e12 q^{79} -1.91379e12 q^{81} -4.25904e12i q^{82} -2.64201e11i q^{83} +8.72709e9 q^{84} +7.12349e11 q^{86} -3.18318e12i q^{87} -1.21958e12i q^{88} +3.69637e12 q^{89} +2.03353e12 q^{91} +1.51070e10i q^{92} -8.57437e12i q^{93} +7.53472e12 q^{94} -3.98834e10 q^{96} +1.00920e13i q^{97} -7.61375e11i q^{98} -5.38510e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 35752 q^{4} + 240752 q^{6} - 2572238 q^{9} - 13208008 q^{11} + 93125856 q^{14} + 399824416 q^{16} - 194982200 q^{19} + 876401472 q^{21} + 7780718400 q^{24} - 7493628088 q^{26} - 4472343700 q^{29}+ \cdots - 253574733016 q^{99}+O(q^{100}) \) 6 * q - 35752 * q^4 + 240752 * q^6 - 2572238 * q^9 - 13208008 * q^11 + 93125856 * q^14 + 399824416 * q^16 - 194982200 * q^19 + 876401472 * q^21 + 7780718400 * q^24 - 7493628088 * q^26 - 4472343700 * q^29 + 14965988752 * q^31 + 60472147976 * q^34 - 86723667704 * q^36 + 140377142144 * q^39 - 21505768868 * q^41 + 136791650336 * q^44 + 493656408672 * q^46 + 77913853258 * q^49 - 258739765888 * q^51 - 492243874400 * q^54 - 1045752902400 * q^56 + 110872847800 * q^59 + 992322785492 * q^61 - 6595130988672 * q^64 - 45767750336 * q^66 + 666758585664 * q^69 + 1043995756672 * q^71 + 4836647173016 * q^74 + 1243376100000 * q^76 - 5981273766400 * q^79 + 641098105526 * q^81 + 1628468261376 * q^84 + 4686627290192 * q^86 + 38846051916900 * q^89 - 13585044740368 * q^91 + 14007115751936 * q^94 - 4416662428928 * q^96 - 253574733016 * q^99

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